Since \(\eta (\cdot )\)  is an admissible function by definition, it
follows that \(L_{2n}(x,\cdot )\)  is an algebraic polynomial of degree
not larger than \(2n\)  for any fixed \(x\in \mathbf {B}^d\) . At the first
glance, as a polynomial kernel, it may have good frequency
localization property while have bad space localization property.
The following Proposition REF , which can be found in
[1]}, however, advocates that \(L_{2n}\) 
is actually a polynomial kernel possessing very good spacial
localized properties. This makes it widely applicable in
approximation theory and signal processing
[2]}, [1]}.
